中点不等式和梯形不等式的量子模拟
|
摘要
建立了涉及二阶q-导数的积分恒等式,使用这个恒等式获得二阶可微函数中点不等式和梯形不等式的量子模拟.
Integral identities related to twice q-derivative are established.Using these identities,some quantum analogues of midpoint inequalities and trapezoid inequalities for twice q-differentiable functions are obtained.
Integral identities related to twice q-derivative are established.Using these identities,some quantum analogues of midpoint inequalities and trapezoid inequalities for twice q-differentiable functions are obtained.
引文
[1]裴礼文.数学分析中的典型问题与方法[M].2版.北京:高等教育出版社,2006:268.
[2]Mitrinovi'c D S.Analytic inequalities[M].New-York:Springer-Verlag,Berlin:Heidelerg,1970.
[3]匡继昌.常用不等式[M].4版.济南:山东科学技术出版社,2010:430-436.
[4]Dragomir S S,Pearce C E M.Selected Topics on Hermite-Hadamard inequalities and applications[D].Victoria:Victoria University,2000.
[5]张小明,褚玉明.解析不等式新论[M].哈尔滨:哈尔滨工业大学出版社,2009:139-148,180-184,198-203,208-212.
[6]王良成.凸函数的Hadamard不等式的若干推广[J].数学的实践与认识,2002,32(6):1027-1030.
[7]文家金,张日新,王挽澜.Hermite-Hadmard不等式的扩张(英文)[J].成都大学学报(自然科学版),2005,24(4):241-247.
[8]柯源,杨斌,胡明旸.Hermite-Hadamard不等式的推广[J].数学的实践与认识,2007,37(23):161-164.
[9]华云.关于GA-凸函数的Hadamard型不等式[J].大学数学,2008,24(2):147-149.
[10]毕燕丽.关于r-预不变凸函数的Hadamard型不等式[J].数学的实践与认识,2009,39(2):190-192.
[11]李觉友.关于s-预不变凸函数的Hadamard型不等式[J].重庆师范大学学报(自然科学版),2010,27(4):5-8.
[12]时统业,尹亚兰,邓捷坤.两类Hadamard型不等式的推广[J].大学数学,2013,29(1):43-47.
[13]黄金莹,赵宇.广义凸函数的Hadamard不等式[J].重庆师范大学学报(自然科学版),2013,30(4):1-5.
[14]程海来.Fejer不等式的注记[J].大学数学,2014,30(1):38-40.
[15]时统业,韦晓萍,周国辉.Fejér不等式加强形式的推广[J].高等数学研究,2016,19(1):39-44.
[16]王国栋.h-F凸函数的一类Hadamard不等式[J].重庆师范大学学报(自然科学版),2014,31(6):1-4.
[17]时统业,尹亚兰,周国辉.严格的Hermite-Hadamard型不等式和Fejér型不等式[J].大学数学,2016,32(1):71-76.
[18]Cerone P,Dragomir S S.Midpoint-type rules from an inequality point of view[M].Handbook of AnalyticComputational Methods in Applied Mathematics,New York:CRC Press,2000:135-200.
[19]Cerone P,Dragomir S S.Trapezoidal-type Rules from an Inequalities Point of View[M].Handbook of AnalyticComputational Methods in Applied Mathematics,New York:CRC Press,2000:65-134.
[20]Sarikaya M Z,Saglam A,Yildirim H.New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are convex and quasi-convex[J].International Journal of Open Problems in Computer Science and Mathematics,2012,5(3):1-14.
[21]Tariboon J,Ntouyas S K.Quantum integral inequalities on finite intervals[J].J.Inequal.Appl.2014,2014(1):1-13.
[22]Stankovi'c M S,Rajkovi'c P M,Marinkovi'c S D.Inequalities which includes q-integrals[J].Bull.Acad.Serbe Sci.Arts,Cl.Sci.Math.Natur.,Sci.Math.,2006,31:137-146.
[23]Tariboon J,Ntouyas S K.Quantum calculus on finite intervals and applications to impulsive difference equations[J].Advances in Difference Equations 2013,2013,article 282.
[24]Marinkovic S,Rajkovi'c P,Stankovi'c M.The inequalities for some types of q-integrals[J].Computers and Mathematics With Applications,2008(56):2490-2498.
[25]Noor M A,Noor K I,Awan M U.Some quantum estimates for Hermite-Hadamard inequalities[J].Applied Mathematics and Comutation,2015,251:675-679.
[26]时统业,李照顺,夏琦.Hermite-Hadamard不等式推广的q-模拟[J].大学数学,2016,32(3):30-36.
[2]Mitrinovi'c D S.Analytic inequalities[M].New-York:Springer-Verlag,Berlin:Heidelerg,1970.
[3]匡继昌.常用不等式[M].4版.济南:山东科学技术出版社,2010:430-436.
[4]Dragomir S S,Pearce C E M.Selected Topics on Hermite-Hadamard inequalities and applications[D].Victoria:Victoria University,2000.
[5]张小明,褚玉明.解析不等式新论[M].哈尔滨:哈尔滨工业大学出版社,2009:139-148,180-184,198-203,208-212.
[6]王良成.凸函数的Hadamard不等式的若干推广[J].数学的实践与认识,2002,32(6):1027-1030.
[7]文家金,张日新,王挽澜.Hermite-Hadmard不等式的扩张(英文)[J].成都大学学报(自然科学版),2005,24(4):241-247.
[8]柯源,杨斌,胡明旸.Hermite-Hadamard不等式的推广[J].数学的实践与认识,2007,37(23):161-164.
[9]华云.关于GA-凸函数的Hadamard型不等式[J].大学数学,2008,24(2):147-149.
[10]毕燕丽.关于r-预不变凸函数的Hadamard型不等式[J].数学的实践与认识,2009,39(2):190-192.
[11]李觉友.关于s-预不变凸函数的Hadamard型不等式[J].重庆师范大学学报(自然科学版),2010,27(4):5-8.
[12]时统业,尹亚兰,邓捷坤.两类Hadamard型不等式的推广[J].大学数学,2013,29(1):43-47.
[13]黄金莹,赵宇.广义凸函数的Hadamard不等式[J].重庆师范大学学报(自然科学版),2013,30(4):1-5.
[14]程海来.Fejer不等式的注记[J].大学数学,2014,30(1):38-40.
[15]时统业,韦晓萍,周国辉.Fejér不等式加强形式的推广[J].高等数学研究,2016,19(1):39-44.
[16]王国栋.h-F凸函数的一类Hadamard不等式[J].重庆师范大学学报(自然科学版),2014,31(6):1-4.
[17]时统业,尹亚兰,周国辉.严格的Hermite-Hadamard型不等式和Fejér型不等式[J].大学数学,2016,32(1):71-76.
[18]Cerone P,Dragomir S S.Midpoint-type rules from an inequality point of view[M].Handbook of AnalyticComputational Methods in Applied Mathematics,New York:CRC Press,2000:135-200.
[19]Cerone P,Dragomir S S.Trapezoidal-type Rules from an Inequalities Point of View[M].Handbook of AnalyticComputational Methods in Applied Mathematics,New York:CRC Press,2000:65-134.
[20]Sarikaya M Z,Saglam A,Yildirim H.New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are convex and quasi-convex[J].International Journal of Open Problems in Computer Science and Mathematics,2012,5(3):1-14.
[21]Tariboon J,Ntouyas S K.Quantum integral inequalities on finite intervals[J].J.Inequal.Appl.2014,2014(1):1-13.
[22]Stankovi'c M S,Rajkovi'c P M,Marinkovi'c S D.Inequalities which includes q-integrals[J].Bull.Acad.Serbe Sci.Arts,Cl.Sci.Math.Natur.,Sci.Math.,2006,31:137-146.
[23]Tariboon J,Ntouyas S K.Quantum calculus on finite intervals and applications to impulsive difference equations[J].Advances in Difference Equations 2013,2013,article 282.
[24]Marinkovic S,Rajkovi'c P,Stankovi'c M.The inequalities for some types of q-integrals[J].Computers and Mathematics With Applications,2008(56):2490-2498.
[25]Noor M A,Noor K I,Awan M U.Some quantum estimates for Hermite-Hadamard inequalities[J].Applied Mathematics and Comutation,2015,251:675-679.
[26]时统业,李照顺,夏琦.Hermite-Hadamard不等式推广的q-模拟[J].大学数学,2016,32(3):30-36.